An aircraft executes a horizontal loop of radius $9 \ km$ at a constant speed of $540 \ kmh^{-1}$. The wings of the aircraft are banked at an angle of (Acceleration due to gravity $g = 10 \ ms^{-2}$)

$A$ particle moves with constant angular velocity in a circular path of a certain radius and is acted upon by a certain centripetal force $F$. If the centripetal force $F$ is kept constant but the angular velocity is doubled,the new radius of the path (original radius $R$) will be:

Two particles of mass $2m$ and $m$ are attached to a light string as shown. The complete system is rotated in a horizontal circle with a constant angular velocity $2\omega$ about an axis passing through point $O$ and perpendicular to the plane of the circle. Find the ratio $T_{OA} / T_{AB}$,where $T_{OA}$ and $T_{AB}$ are the tensions in strings $OA$ and $AB$ respectively.

$A$ conical pendulum of length $1\,m$ makes an angle $\theta = 45^\circ$ with respect to the $Z$-axis and moves in a circle in the $XY$ plane. The radius of the circle is $0.4\,m$ and its centre is vertically below $O$. The speed of the pendulum,in its circular path,will be ..... $m/s$ (Take $g = 10\,ms^{-2}$)

$A$ dumbbell is placed on a frictionless horizontal table. Sphere $A$ is attached to a frictionless pivot so that $B$ can be made to rotate about $A$ with constant angular velocity. If $B$ (mass $2M$) makes one revolution in period $P$,the tension in the rod (length $d$) is

$A$ particle of mass $m$ is suspended from a ceiling through a string of length $L$. If the particle moves in a horizontal circle of radius $r$ as shown in the figure,then the speed of the particle is